Which data should be tracked in forward-dynamic optimisation to best predict muscle forces in a pathological co-contraction case?

The choice of the cost-function for predicting muscle forces during a movement remains a challenge, especially in patients with neuromuscular disorders. Forward dynamics-based optimisations mainly track joint kinematics or torques, combined with a least-excitation criterion. Tracking marker trajectories and/or electromyography (EMG) has rarely been proposed. Our objective was to determine the best tracking objective-function to accurately predict the upper-limb muscle forces. A musculoskeletal model was created and EMG was simulated to obtain a reference movement – a shoulder abduction. A Gaussian noise (mean = 0; standard deviation = 15%) was added to the simulated EMG. Another noise – corresponding to the actual soft tissue artefacts (STA) of experimental shoulder abduction movements – was added to the trajectories of the markers placed on the model. Muscle forces were estimated from these noisy data, using forward dynamics assisted by six non-linear least-squared objective-functions. These functions involved the tracking of marker trajectories, joint angles or torques, with and without EMG-tracking. All six approaches used the same musculoskeletal model and were solved using a direct multiple shooting algorithm. Finally, the predicted joint angles, muscle forces and activations were compared to the reference values, using root-mean-square errors (RMSe) and biases. The force RMSe of the approach tracking both marker trajectories and EMG (18.45 ± 12.60 N) was almost five times lower than the one of the approach tracking only joint angles (82.37 ± 66.26 N) or torques (85.10 ± 116.40 N). Therefore, using EMG as a complementary tracking-data in forward dynamics seems to be promising for the estimation of muscle forces.